The probability of a man hitting the target at a shooting range is $\frac{1}{4}$. If he shoots 10 times, what is the probability that he hits the target at least once?

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13-08-2024
Mathematics

High School

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The probability of a man hitting the target at a shooting range is $\frac{1}{4}$. If he shoots 10 times, what is the probability that he hits the target at least once?

Answer :

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TaylorSmith46 TaylorSmith46 · Answer 1 · 2023-08-22T08:54:03-04:00

To find the probability of a man hitting a target at least once in 10 shots with an individual shot probability of 1/4, calculate 1 - (3/4)^10, which is approximately 0.9437 or 94.37%.

The probability of a man hitting the target at least once can be calculated by finding the probability of the complementary event, which is the man not hitting the target at all during the 10 shots, and then subtracting it from 1. The probability of missing the target in one shot is 1 - 1/4 = 3/4. Therefore, the probability of not hitting the target at all in 10 shots is (3/4)^10. The probability of hitting the target at least once is thus 1 - (3/4)^10.

First, calculate the probability of not hitting the target at all in 10 shots:

Probability of missing once = 3/4
Probability of missing 10 times = (3/4)^10

Next, subtract this value from 1 to find the probability of hitting the target at least once:

Probability of hitting at least once = 1 - (3/4)^10

Calculate the probability: 1 - (3/4)^10 ≈ 1 - 0.0563 ≈ 0.9437

So, the man has a probability of approximately 0.9437, or 94.37%, of hitting the target at least once in 10 shots.

The probability of a man hitting the target at a shooting range is \(\frac{1}{4}\). If he shoots 10 times, what is the probability that he hits the target at least once?

Answer :

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